There's different ways. To find your external ip see http://www.whatismyip.com/

BUT, if you're wanting to direct connect to someone then if you select the direct connect type search then your ip address should be listed above the search box. If it isn't then it means that you're firewalled (not properly configured) & direct connect would never work. You need to ensure you're configured properly. Your software firewall, & ensure your modem/router has UPnP enabled. See instructions here Connection problems? Check here first! (click on link)

To test if you're firewalled, look at the globe icon at the bottom of LW, does it have a wall in front of it? If yes then you have configuring to do. Another method to test is this: Do this test: Bug Report instructions & sample image Is the result True/False? If false, then you're not properly configured, if true then you're fine.

More on direct connect here: How to use Direct Connect. BTW you can also send magnet links to a friend to connect & you can each browse each other via the upload & downld windows.